Considerable debate exists over the kinds of numbers the Approximate Number System (ANS) can represent and compute over. Across three experiments (N = 218), we show that children can represent and add large mixed sets (i.e., large collections that include two types of items) with the ANS. In Experiment 1, 5-7-year-olds completed a replication of a large non-symbolic number addition task using an online asynchronous format. In Experiments 2 and 3, 5-7-year-olds completed a variation of that addition task with mixed sets of stimuli either area-controlled or area-correlated and again performed above chance level. Taken together, these findings are a crucial first step in examining whether the ANS can represent all positive rational numbers (i.e., fractions or ratios), as opposed to exclusively integers. In sum though, our findings suggest that children can represent and compute over large mixed sets of stimuli with the ANS.